find the average rate of hange for the function f(x)=2 cos(x^2) on the interval [1,3]

Answer:

$6.57

Step-by-step explanation:

Answer:

6.57

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

It is very simple, just multiply the principal amount by the interest rate:

a: 2500 x 0.018 = £45

b: 2500 x 0.021 = £52.50

c: 2500 x 0.024 = £60

(a) In trade equilibrium, the consumption point for the Home consumer can be shown on a graph where wheat is on the x-axis.

(b) If the world relative price increases above 2/3, the Foreign consumer's utility will decrease compared to the benchmark trade equilibrium with a world price of 2/3.

a, Since the relative price of wheat to cloth is 2/3, the Home consumer's consumption point will lie on a budget line with a slope of -2/3. The specific coordinates of the consumption point cannot be determined without additional information about preferences and the Home consumer's budget constraint.

To show that an increase in the relative price of wheat from 2/3 raises Home's utility, we need to consider the concept of substitution effect. When the relative price of wheat increases, it becomes relatively more expensive compared to cloth. The Home consumer will respond by consuming less wheat and more cloth, moving along the budget line to a new consumption point. This movement is driven by the substitution effect, where the consumer substitutes away from the now relatively more expensive wheat towards the relatively cheaper cloth. Since the Home consumer's preferences and utility are not known, the specific utility level cannot be quantified, but it can be concluded that the utility increases due to the substitution effect.

b.  In the benchmark equilibrium, the Foreign consumer maximizes utility given the initial relative price. If the relative price increases, it means that wheat becomes relatively more expensive compared to cloth in the world market.

As a result, the Foreign consumer will have to consume less wheat and more cloth in order to remain on the same budget line. This movement along the budget line leads to a decrease in utility because the consumer has to give up some desired wheat consumption to obtain more cloth. The magnitude of the utility decrease depends on the specific preferences and utility function of the Foreign consumer, but it can be concluded that the utility will be lower when the relative price of wheat increases above 2/3 in the world market.

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If asking how many 1/2 a yard(s) are in a whole yard your answer is 2, because 1/2 + 1/2 = 1

We can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26.

Based on the given information, we can calculate a 95% confidence interval for the mean amount that women in the population spend dining out per week. With a sample size of 25 and a standard error of $4, we can use the formula:

95% CI = sample mean +/- (critical value x standard error)

To find the critical value, we need to look up the t-distribution with degrees of freedom (df) = n-1 = 24 and a significance level of alpha = 0.05/2 = 0.025 (since we are interested in a two-tailed test). From a t-table or calculator, we find that the critical t-value is approximately 2.064.

Plugging in the values, we get:

95% CI = $100 +/- (2.064 x $4)
95% CI = $100 +/- $8.26
95% CI = ($91.74, $108.26)

Therefore, we can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26. This means that if we were to repeatedly take random samples of 25 women and calculate their mean amount spent dining out, about 95% of the intervals we construct using this method would contain the true population mean.

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By using the fact that the two angles whose measures are expressed in terms of x are vertical angles, we will see that x = 8.

Then using that we will see that the measure of angle BAC is 63 degrees.

On the given diagram, we can see that the two angles whose measures are expressed in terms of x are vertical angles, thus, these two angles have the same measure, then we can write a linear equation that helps us to find the value of x, which is:

(2x + 3) = (4x - 5)

Solving the linear equation for x we get:

2x + 3 = 4x - 5

3 + 5 = 4x - 2x

8 = 2x

8/2 = x = 4

So we can see that the value of x is 4.

Now we want to find the measure of angle BAC.

We can see that the measure of angle BAC plus the measure of the angle to its right will be a right angle, then we can write:

m∠BAC + (4x - 5)° = 90°

Replacing the value of x we get:

m∠BAC + (4*8 - 5)° = 90°

m∠BAC + 27° = 90°

m∠BAC = 90° - 27° = 63°

We conclude that the measure of angle BAC is 63 degrees.

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Answer: Rs 25,000

Step-by-step explanation:

Given

Retailer sold an electric iron to a customer at a loss of 10%

Suppose the Cost price of iron is \(x\)

So, selling price is \(0.9x\)

This price must be equal to \(25425\)+ VAT

\(\Rightarrow 0.9x=25425-0.13(0.9x)\\\Rightarrow 0.9x+0.117x=25425\\\Rightarrow 1.017x=25425\\\Rightarrow x=\text{Rs }25,000\)

Thus, the cost price is \(Rs.25,000\)

Answer:

0.1

Step-by-step explanation:

Answer:

0.4 ÷ 4 = 0.1

Explanation:

Answer:

to be entirely honest i do not know

Step-by-step explanation:

Answer:

X − 4.2

Step-by-step explanation:

Answer:

x - 4.2

Step-by-step explanation:

x + 1 - 1 = x

so x - 4.2 is the simplest i believe <3

Answer:

The answer is 0.

Search up "Linear Equation Calculator" and use one of those to get the work.

Answer:

No solution

Step-by-step explanation:

3(1-2x)>3-6x

3-6x > 3-6x

3            3

The offer percentage on that online site on the book  is 20%

What is the dollar amount of discount?

The dollar value of the discount given by the online site is difference between the normal price of the  book which is $25 and the offer price of the online site of $20 as shown below:

discount offered=$25-$20

discount offered=$5

Now that the offer discount has been ascertained, the discount offer in percentage terms relates the dollar value of the discount to the normal price to arrive at the percentage given off the normal price

offer percentage=discount offered/normal selling price

offer percentage=$5/$25

offer percentage=20%

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Answer:

A square and maybe a kite.

Step-by-step explanation:

Answer:

D. Square

Step-by-step explanation:

Here is a good images that explains what is what:

Read it from bottom to top. It cannot be reversed.

Answer:

cos(52.5°)sin(7.5°)

sin(52.5°)sin(7.5°)

cos(52.5°)cos(7.5°)

sin(52.5°)cos(7.5°)

In increasing order , the expressions are written as follows , cos(52.5°)sin(7.5°) , sin(52.5°)sin(7.5°) , cos(52.5°)cos(7.5°) , sin(52.5°)cos(7.5°).

Statements that have more than one term and a variable is connected to another variable by a mathematical operator are called Expressions.

The expression given are

cos(52.5°)cos(7.5°)

sin(52.5°)cos(7.5°)

sin(52.5°)sin(7.5°)

cos(52.5°)sin(7.5°)

To arrange them into increasing order , the value of it has to be determined.

cos(52.5°)cos(7.5°) = 0.6088 * 0.9914 = 0.6036

sin(52.5°)cos(7.5°)= 0.7933*0.9914 = 0.7865

sin(52.5°)sin(7.5°)= 0.7933*0.1305 = 0.1035

cos(52.5°)sin(7.5°)= 0.6088*0.1305= 0.07945

Therefore in Increasing order , the expressions are written as follows , cos(52.5°)sin(7.5°) , sin(52.5°)sin(7.5°) , cos(52.5°)cos(7.5°) , sin(52.5°)cos(7.5°).

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The statement concerning the binomial distribution that is correct is: "Its CDF shows the probability of each value of X."A binomial distribution is a probability distribution that describes the probability of k successes in n independent Bernoulli trials, where p is the probability of success in any one trial. The probability density function (PDF) of the binomial distribution is given by: P (X = k) = (n k)pk(1−p)n−k, Where X is the random variable representing the number of successes, p is the probability of success, and n is the number of trials. The cumulative distribution function (CDF) of the binomial distribution, on the other hand, gives the probability of obtaining a value less than or equal to x. Therefore, the correct statement concerning the binomial distribution is: "Its CDF shows the probability of each value of X. "Option A, "Its CDF is skewed right when π < 0.50," is incorrect because the skewness of the binomial distribution depends on both n and p, not just p. Option C, "Its PDF covers all integer values of X from 0 to n," is also incorrect because the binomial distribution only covers integer values of X from 0 to n, not necessarily all of them. Finally, option D, "Its PDF is the same as its CDF when π = 0.50," is incorrect because the PDF and CDF of the binomial distribution are different for any value of p, not just when p = 0.50.

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If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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Answer:

5/4

Step-by-step explanation:

Slope is y1-y2/x1-x2 so if you plug in the coordinates you get 4-(-1)/4-0 which you would get 5/4

Answer: 12x

Step-by-step explanation:

(

2

+

3

)

(

2

−

1

)

=

1

0

2

(

+

8

)

2

−

9

=

5

2

3

1

5

+

(

+

2

)

=

1

0

4

(

−

4

)

=

3

2

5

3

(

−

2

)

=

1

2

a) The present value of $25,000 due 9 periods from now, discounted at 10%, is approximately $10,593.22.

b) The present value of $25,000 to be received at the end of each of 6 periods, discounted at 9%, is approximately $22,935.35.

(a) Present Value of $25,000 due 9 periods from now, discounted at 10%:

To calculate the present value, we need to discount the future cash flow of $25,000 back to its current value using the given discount rate of 10%. The formula to calculate the present value is:

Present Value = Future Value / (1 + Discount Rate)ⁿ

Where:

Future Value is the amount to be received in the future ($25,000).

Discount Rate is the rate at which we discount the future cash flow (10%).

'n' is the number of periods or years until the future cash flow is received (9 periods in this case).

Let's plug in the values into the formula and calculate the present value:

Present Value = $25,000 / (1 + 0.10)⁹

Calculating the denominator:

(1 + 0.10)⁹ = 1.10⁹ ≈ 2.36

Present Value = $25,000 / 2.36 ≈ $10,593.22

(b) Present Value of $25,000 to be received at the end of each of 6 periods, discounted at 9%:

In this case, we have a cash flow of $25,000 to be received at the end of each of 6 periods, discounted at 9%. Let's calculate the present value:

Present Value = $25,000 / (1 + 0.09)¹ + $25,000 / (1 + 0.09)² + ... + $25,000 / (1 + 0.09)^6

Calculating each discount factor:

(1 + 0.09)¹ ≈ 1.09

(1 + 0.09)² ≈ 1.1881

(1 + 0.09)³ ≈ 1.2950

(1 + 0.09)⁴ ≈ 1.4116

(1 + 0.09)⁵ ≈ 1.5386

(1 + 0.09)⁶ ≈ 1.6765

Plugging in the values and summing them up:

Present Value = $25,000 / 1.09 + $25,000 / 1.1881 + $25,000 / 1.2950 + $25,000 / 1.4116 + $25,000 / 1.5386 + $25,000 / 1.6765

Present Value ≈ $22,935.35

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The probability of three successful surgeries is 0.421875, the probability of none of the three surgeries being successful is 0.015625, and these events are not complementary.

Given that the probability of a particular surgery being successful is 0.75, we can calculate the probabilities of specific outcomes using the binomial distribution. We need to find the probability of three successful surgeries and the probability of none of the three surgeries being successful. Additionally, we will determine if these events are complementary.

a) To find the probability that three surgeries are successful, we use the binomial distribution formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of surgeries, k is the number of successful surgeries, and p is the probability of success. Plugging in the values, we have P(X=3) = C(3, 3) * 0.75^3 * (1-0.75)^(3-3) = 0.421875.

b) To find the probability that none of the three surgeries are successful, we use the same binomial distribution formula. P(X=0) = C(3, 0) * 0.75^0 * (1-0.75)^(3-0) = 0.015625.

c) Two events are considered complementary if the sum of their probabilities is equal to 1. In this case, the event of three successful surgeries and the event of none of the three surgeries being successful are complementary. The probability of three successful surgeries (0.421875) plus the probability of none of the surgeries being successful (0.015625) equals 0.4375, which is less than 1. Therefore, the events are not complementary.

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Answer:

33

Step-by-step explanation:

Answer:

29c

Step-by-step explanation:

The area enclosed by the curve r = 9 + 2cos(θ) is 45π square units.

To find the area enclosed by the curve r = 9 + 2cos(θ), we can use the formula for the area enclosed by a polar curve, which is given by:

A = (1/2) \(\int\limits^a_b\) r(θ)^2 dθ

where a and b are the values of θ that correspond to the starting and ending points of the area we want to calculate.

In this case, since the curve r = 9 + 2cos(θ) describes a closed loop, we can choose a range of θ that covers the entire loop, for example, [0, 2π]. Therefore, the area enclosed by the curve is

A = (1/2)\(\int\limits^{2\pi }_0\) (9 + 2cos(θ))^2 dθ

Expanding the square and using the trigonometric identity cos^2(θ) = (1/2)(1 + cos(2θ)), we get

A = (1/2) \(\int\limits^{2\pi }_0\) (81 + 36cos(θ) + 4cos^2(θ)) dθ

= (1/2) \(\int\limits^{2\pi }_0\) (81 + 36cos(θ) + 2 + 2cos(2θ)) dθ

= (1/2) (81(2π) + 36sin(θ)|[0,2π] + 2θ|0,2π + sin(2θ)|[0,2π])

= 45π square units

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The given question is incomplete, the complete question is:

Find the area enclosed by the curve r = 9 + 2cos(θ)

The precision of the estimate decreases when standard error of an estimate when the sample size in a SRS decreases. So, the correct answer is D).

The standard error of an estimate measures the variability of sample means around the population mean. As the sample size in a simple random sample (SRS) decreases, the sample mean becomes less representative of the population mean, resulting in more variability or less precision in the estimate.

The standard error increases as the sample size decreases because there is more uncertainty in the estimate due to the smaller sample size. Therefore, decreasing the sample size will increase the margin of error and decrease the precision of the estimate. So, the correct option is D).

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Answer:

Final solution is ---> 17

See attached picture for step-by-step explanation

Answer:

17

Step-by-step explanation:

A fraction bar is like parentheses

Complete the  items above and below it first

43-1

------- + 10

4+2

42

----- + 10

6

Then divide

7+10

Then add

17

The price per foot of the plastic wrap equals to $0.54.

Generally, a price per square foot is mostly calculated by taking the figure for property price and dividing it by the total square footage of the living space. The typical formula for Price per square foot = price / floor space in ft².

Given that the 6-yard roll of plastic wrap costs $9.72. Then, 1 yard of plastic equals to $1.62.

Because 1 yard equals 3 feet, then, the price per foot of the plastic wrap will be gotten as follows:

= 1/3 * $1.62

= $0.54

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Answer:

To determine which ball weighs more, we need to know the density of zinc and chromium. The density of zinc is **7.14 g/cm³** and the density of chromium is **7.19 g/cm³**. The volume of a sphere is given by the formula `V = (4/3)πr³`, where `r` is the radius of the sphere. So, the volume of the zinc ball with a radius of 3 cm is `V = (4/3)π(3)³ ≈ 113.1 cm³`, and the volume of the chromium ball with a radius of 2.99 cm is `V = (4/3)π(2.99)³ ≈ 112.1 cm³`. The mass of an object is given by the formula `m = ρV`, where `ρ` is the density of the material and `V` is the volume of the object. So, the mass of the zinc ball is `m = (7.14 g/cm³)(113.1 cm³) ≈ 807.6 g`, and the mass of the chromium ball is `m = (7.19 g/cm³)(112.1 cm³) ≈ 806.1 g`. Therefore, **the ball of zinc weighs more** than the ball of chromium.

Answer:

A ball of zinc.

Step-by-step explanation:

Density is defined as the ratio of an object's mass to its volume.

The formula for density is:

\(\large\boxed{\rho = \dfrac{m}{V}}\)

where:

Therefore, to calculate the weight of each ball, multiply its volume by the density of the material.

A ball can be modelled as a sphere. Therefore, calculate the volumes of the balls by using the formula for the volume of a sphere.

\(\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Substitute the respective values of r into the formula to calculate the volumes of the two balls.

\(\begin{aligned}\textsf{Volume of the ball of zinc}&=\dfrac{4}{3} \pi (3)^3\\\\&=\dfrac{4}{3} \pi (27)\\\\&=36\pi\\\\&=113.0973355292... \; \sf cm^3\end{aligned}\)

\(\begin{aligned}\textsf{Volume of the ball of chronium}&=\dfrac{4}{3} \pi (2.99)^3\\\\&=\dfrac{4}{3} \pi (26.730899)\\\\&=35.6411986666...\pi\\\\&= 111.9701278963...\; \sf cm^3\end{aligned}\)

The density of zinc (Zn) is approximately 7.14 g/cm³.

The density of chromium (Cr) is approximately 7.15 g/cm³.

Therefore, the approximate weights of the two balls are:

\(\begin{aligned}\textsf{Weight of the ball of zinc}&=113.0973355292... \times 7.14\\&=807.514975...\\&=807.51 \; \sf g\end{aligned}\)

\(\begin{aligned}\textsf{Weight of the ball of chronium}&= 111.9701278963... \times 7.15\\&=800.586414...\\&=800.59\; \sf g\end{aligned}\)

As 807.51 > 800.59, a ball of zinc with a radius of 3 cm weighs more than a ball of chromium with a radius of 2.99 cm.

Answer:

Step-by-step explanation:

2x+3y=6. Subtract 2x from each side to get 3y by itself. 3y=-2x+6. Divide by 3 on each side to cancel out the 3 from the y. y=-2/3x+2.

-3x-5y=-12. Add 3x to each side to get -5y by itself. -5y=3x-12. Divide each side by -5 to cancel out the -5 from the y. y=-3/5x+12/5.

Write both of them as if the are equal to each other.

-2/3x+2=-3/5x+12/5. subtract 12/5 from each side and add -2/3 to each side.

0=1/15x+2/5. Subtract 2/5 from each side

-2/5=1/15x. Divide by 1/15 to get "x="

-6=x and y=6.

Check your solution by subsituting in numbers in place for your variables.

2(-6)+3(6)=6

-3(-6)-5(6)=-12

Hope this helps. Always remember to check your solution.

Answer:

x = 12

Step-by-step explanation:

The midsegment VY is half the sum of the parallel bases , that is

VY = \(\frac{EF+CD}{2}\) , then

3x + 18 = \(\frac{1}{2}\) (x + 96) ← multiply both sides by 2 to clear the fraction

6x + 36 = x + 96 ( subtract x from both sides )

5x + 36 = 96 ( subtract 36 from both sides )

5x = 60 ( divide both sides by 5 )

x = 12